plot::Cone

Cones and frustums

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Syntax

plot::Cone(br, [bx, by, bz], <tr>, [tx, ty, tz], <a = amin .. amax>, options)

Description

plot::Cone(br, [ bx, by, bz], [ tx, ty, tz]) creates a cone stretching from the base with radius br and center [bx, by, bz] to the top [tx, ty, tz].

plot::Cone(br, [ bx, by, bz], tr, [ tx, ty, tz]) creates a conical frustum from the base center [bx, by, bz] to the top center [tx, ty, tz]. The base radius is br, the top radius is tr.

The lower center and upper center of the cone can also be passed as vectors.

The optional “top radius” tr for creating a frustum may also be specified as the attribute TopRadius = tr.

The upper and lower faces of a cone/frustum are not filled. They can be added as filled plot::Circle3ds.

Note that only circular cones can be created with plot::Cone. For elliptical bases, use a plot::Surface primitive or apply a plot::Scale3d transformation.

Attributes

AttributePurposeDefault Value
AffectViewingBoxinfluence of objects on the ViewingBox of a sceneTRUE
Basebase center of cones, cylinders, pyramids and prisms[0, 0, 0]
BaseXx-coordinate of top center of cones, cylinders, pyramids and prisms0
BaseYy-coordinate of top center of cones, cylinders, pyramids and prisms0
BaseZz-coordinate of top center of cones, cylinders, pyramids and prisms0
BaseRadiusbase radius of cones/conical frustums and pyramids/frustums of pyramids1
Colorthe main colorRGB::LightBlue
Filledfilled or transparent areas and surfacesTRUE
FillColorcolor of areas and surfacesRGB::LightBlue
Framesthe number of frames in an animation50
Legendmakes a legend entry 
LegendTextshort explanatory text for legend 
LegendEntryadd this object to the legend?FALSE
LineColorcolor of linesRGB::Black.[0.25]
LineWidthwidth of lines0.35
LineStylesolid, dashed or dotted lines?Solid
LinesVisiblevisibility of linesTRUE
LineColorDirectionthe direction of color transitions on lines[0, 0, 1]
LineColorDirectionXx-component of the direction of color transitions on lines0
LineColorDirectionYy-component of the direction of color transitions on lines0
Namethe name of a plot object (for browser and legend) 
ParameterEndend value of the animation parameter 
ParameterNamename of the animation parameter 
ParameterBegininitial value of the animation parameter 
ParameterRangerange of the animation parameter 
Shadingsmooth color blend of surfacesSmooth
TimeEndend time of the animation10.0
TimeBeginstart time of the animation0.0
TimeRangethe real time span of an animation0.0 .. 10.0
Titleobject title 
TitleFontfont of object titles[" sans-serif ", 11]
TitlePositionposition of object titles 
TitleAlignmenthorizontal alignment of titles w.r.t. their coordinatesCenter
TitlePositionXposition of object titles, x component 
TitlePositionYposition of object titles, y component 
TitlePositionZposition of object titles, z component 
Toptop center of cones, cylinders, pyramids and prisms[0, 0, 1]
TopXbase and top center of cones, cylinders, pyramids and prisms0
TopYbase and top center of cones, cylinders, pyramids and prisms0
TopZbase and top center of cones, cylinders, pyramids and prisms1
TopRadiustop radius of cones/conical frustums and pyramids/frustums of pyramids0
VisiblevisibilityTRUE
VisibleAfterobject visible after this time value 
VisibleBeforeobject visible until this time value 
VisibleFromToobject visible during this time range 
VisibleAfterEndobject visible after its animation time ended?TRUE
VisibleBeforeBeginobject visible before its animation time starts?TRUE

Examples

Example 1

We draw a cone with base radius 6:

plot(plot::Cone(6, [0, 0, 0], [0, 0, 10])):

Example 2

We create a conical frustum by specifying a non-zero top radius. Note that no discs are attached to the base and the top. You can look through the frustum:

br := 16: base := [3, 4, 5]:
tr:= 7: top := [11, 12, 13]:
plot(plot::Cone(br, base, tr, top, FillColor = RGB::Red)):

We add the discs at the base and the top. Their normals n are given as the vector from the base to the top:

n := zip(top, base, _subtract):
plot(plot::Circle3d(br, base, n, Filled = TRUE),
     plot::Circle3d(tr, top, n, Filled = TRUE),
     plot::Cone(br, base, tr, top),
     LinesVisible = FALSE, FillColor = RGB::Red):

delete br, base, tr, top, n:

Example 3

A tube or cylinder (in the mathematical sense, i.e., the lateral sides of a physical cylinder) is a special case of a conical frustum with the same top and bottom radius:

plot(plot::Cone(6, [0, 0, 0], 6, [11, 12, 13],
                FillColor = RGB::Yellow,
                LinesVisible = TRUE)):

Example 4

Bottom and top radii and centers can be animated:

plot(plot::Cone(sin(a)^2, [sin(2*a), cos(2*a), 0],
                cos(a)^2, [cos(2*a), sin(2*a), 1],
                a = 0..PI, FillColor = RGB::Green)):

Parameters

br

The base radius of the cone. This must be a real numerical value or an arithmetical expression of the animation parameter a.

br is equivalent to the attribute BaseRadius.

bx, by, bz

The lower center point. The coordinates bx, by, bz must be real numerical values or arithmetical expressions of the animation parameter a.

bx, by, bz are equivalent to the attributes BaseX, BaseY, BaseZ.

tr

The top radius of the cone/conical frustum. This must be a real numerical value or an arithmetical expression of the animation parameter a. If no top radius is specified, a cone with top radius tr = 0 is created.

tr is equivalent to the attribute TopRadius.

tx, ty, tz

The upper center point. The coordinates tx, ty, tz must be real numerical values orarithmetical expressions of the animation parameter a.

tx, ty, tz are equivalent to the attributes TopX, TopY, TopZ.

a

Animation parameter, specified as a = amin..amax, where amin is the initial parameter value, and amax is the final parameter value.

See Also

MuPAD Functions

MuPAD Graphical Primitives